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Pyroxene Mineral Formula
Sheet1
Oxide Mineral Calculation
Clinopyroxene 91145
Col 1Col 2Col 3Col 4Col 5
Wt% OxMol WtMol OxAt Ox# anionsCationsIVVI
50.5260.090.84071.68153.8301.911.91
0.2879.90.00350.00700.0160.010.01
2.77101.940.02720.08150.1860.120.080.05
159.70.00000.00000.0000.000.00
FeO10.9471.850.15230.15230.3470.350.35
MnO0.2370.940.00320.00320.0070.010.01
MgO12.6340.320.31320.31320.7130.710.71
CaO21.7556.080.38780.38780.8830.880.88
0.4861.980.00770.00770.0180.040.04
94.20.00000.00000.0000.000.00
99.602.63432.001.99
# O's =6WoEnFs
0.880.710.35
E17/E16 =2.2776453718
Orthopyroxene 91145
Col 1Col 2Col 3Col 4Col 5
Wt% OxMol WtMol OxAt Ox# anionsCationsIVVI
52.0960.090.86691.73373.9191.961.96
0.1279.90.00150.00300.0070.000.00
1.63101.940.01600.04800.1090.070.040.04
159.70.00000.00000.0000.000.00
FeO27.0671.850.37660.37660.8580.860.86
MnO0.6670.940.00930.00930.0210.020.02
MgO19.1140.320.47400.47401.0791.081.08
CaO0.5156.080.00910.00910.0210.020.02
0.0561.980.00080.00080.0020.000.00
94.20.00000.00000.0000.000.00
101.232.65452.001.98
# O's =6WoEnFs
0.021.080.86
E37/E36 =2.260315644
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Paulings Rulesfor Ionic CrystalsDeal with the energy state of
the crystal structure
1st RuleThe cation-anion distance = radii
Can use RC/RA to determine the coordination number of the
cation
This is our previous discussion on coordination polyhedra
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Paulings Rulesfor Ionic Crystals2nd RuleFirst note that the
strength of an electrostatic bond = valence / CN
Na+ in NaCl is in VI coordination
For Na+ the strength = +1 divided by 6 = + 1/6ClClClClNa
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Paulings Rulesfor Ionic Crystals2nd Rule: the electrostatic
valence principle+ 1/6+ 1/6+ 1/6+ 1/6NaNaNaNaCl-An ionic structure
will be stable to the extent that the sum of the strengths of
electrostatic bonds that reach an anion from adjacent cations = the
charge of that anion
6 ( + 1/6 ) = +1 (sum from Nas)charge of Cl = -1
These charges are equal in magnitude so the structure is
stable
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Paulings Rules3rd Rule:The sharing of edges, and particularly of
faces, of adjacent polyhedra tend to decrease the stability of an
ionic structureFig 9-18 of Bloss, Crystallography and Crystal
Chemistry. MSA
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Paulings Rules4th Rule:In a crystal with different cations,
those of high valence and small CN tend not to share polyhedral
elements
An extension of Rule 3Si4+ in IV coordination is very unlikely
to share edges or faces
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Paulings Rules5th Rule:The number of different kinds of
constituents in a crystal tends to be small
Using the analogy of CP oxygens this rule states that the number
of types of interstitial sites that are filled in a regular and
periodic array tends to be small
4 common types of cation sites in such an array:XII (large
cations replace O positions)VI VIII is not CPIVIII (small and
uncommon cations)
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Paulings Rules5th Rule:Cant fill both (share face)HCPIV sitesVI
sitesVI and IV sites in HCP array of oxygen anions(not all will be
occupied due to charge balance)
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Paulings Rules5th Rule:CCPIV sitesVI sitesVI and IV sites in CCP
array of oxygen anions(not all will be occupied due to charge
balance)
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Paulings Rules5th Rule:The spinel structure at various
angles
NoteCCP abcabc layers of OxygensWhite VI sitesBlue IV sites
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Paulings Rules5th Rule:The spinel structure at various
anglesPolyhedral modelWhite VI sitesBlue IV sites
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Paulings Rules5th Rule:The spinel structure at various anglesNow
see lines of VI and IV sitesNot all are occupied 1/8 of IV sites
1/2 of VI sites
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Paulings Rules5th Rule:The spinel structure at various
anglesRotating to where cation sites almost line up
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Paulings Rules5th Rule:The spinel structure at various
anglesThis orientation is looking down (010)It makes an excellent
projection, since atoms all stack up on top of one another toward
you The order becomes apparentBut you lose the third dimension
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Two miscellaneous structural conceptsIsostructuralismMinerals
with the same structure, but different compositionsCaF2 - BaCl2
AntistructuralismMinerals with the same struture, but one has
cations where the other has anions and vice-versaCaF2 - Na2O
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PolymorphismDifferent structural forms for compounds of the same
composition different mineralsThe compound SiO2 has several
different structural forms, or polymorphsThe common form is - or
low-quartz, but there are others that become stable under different
conditions, including - or high-quartz, tridymite, cristobalite,
coesite, and stishoviteThe SiO2 phase diagram After Swamy and
Saxena (1994) J. Geophys. Res., 99, 11,787-11,794.
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Polymorphism
1. Displacive polymorphism quartz at 573oC at atmospheric
pressure
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Polymorphism
1. Displacive polymorphismNote: higher T higher symmetry due to
more thermal energy (may twin as lower T)Transition involves small
adjustments and no breaking of bondsEasily reversed and
non-quenchable (low E barrier)HighLowP6222P3221
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Polymorphism
2. Reconstructive polymorphsMore common: other quartz
polymorphs, graphite-diamond, calcite-aragonite,
sillimanite-kyanite-andalusiteTransition involves extensive
adjustments, including breaking and reformation of bondsHigh E
barrier, so quenchable and not easily reversed (still find
Precambrian tridymite)StableUnstableMetastable
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Pseudorphism
May be confused with polymorphsA completely different
thingComplete replacement of one mineral by one or more other
minerals such that the new minerals retain the external shape of
the original oneLimonite after pyriteChlorite after garnetetc.Can
use the shape to infer the original mineralVery useful in
petrogenetic interpretations
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Solid Solutions
Substitution (mixing, solution) of ions on specific
sitesForsterite: Mg2SiO4Mg occupies the VI sites in the olivine
structureCan substitute Fe for Mg and create Fayalite: Fe2SiO4In
olivine the substitution is very readily accomplished and any
intermediate composition is possibleOlivine: (Mg, Fe)2SiO4This
means that olivine is a solid-solution series in which any ratio of
Mg/Fe is possible as long as they sum to two ions per formula unit
(required for electric neutrality)
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Solid Solutions
Intermediate compositions can be expressed as:1. A chemical
analysis (in weight % oxides)SiO238.5FeO22.9MgO38.6Total 100.0Such
an analysis is very difficult to interpret in terms of the mineral
that it represents
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Solid Solutions
Intermediate compositions can be expressed as:1. A chemical
analysis (in weight % oxides)SiO238.5FeO22.9MgO38.6Total 100.02.
This can be converted to a mineral formulaMg1.5 Fe0.5 SiO4Such an
analysis is very difficult to interpret in terms of the mineral
that it represents
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Solid Solutions
Intermediate compositions can be expressed as:1. A chemical
analysis (in weight % oxides)SiO238.5FeO22.9MgO38.6Total 100.02.
This can be converted to a mineral formulaMg1.5 Fe0.5 SiO43. This
can then be expressed in terms of end-membersXMg = Mg / (Mg + Fe)
on an atomic basis = 1.5 / 2 = 0.75orFo75 where the sum of the
end-members = 1(Fo75 implies Fa25)Such an analysis is very
difficult to interpret in terms of the mineral that it
represents
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Solid Solutions
Solid solutions are most extensive if the valence and radius of
the substituting ions are similarGood if radii differ by < 15%Fe
2+ = 0.80 A Mg 2+ = 0.74 A (7.5%)Mn 2+ = 0.91 A (14% - Fe and 21% -
Mg)Limited or rare if differ by 15-30 %Never if > 30 %
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Solid Solutions
Solid solutions are most extensive if the valence and radius of
the substituting ions are similarIf valence differs will not
substitute or requires coupled substitutionNaAlSi3O8 - CaAl2Si2O8
in plagioclaseNa+ + Si4+ exchange for Ca2+ + Al3+ to maintain 5+
total
Jadeite NaAlSi2O6 - diopside CaMgSi2O6
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ExsolutionLower TLimits impurityStructure may reject
excessExsolutionOriented lamellae, orEntirely rejected from the
crystalNon-coherent masses
As temperature drops, the decreasing thermal energy in the
lattice, the tolerance of one end-member for the complementary ion
becomes lessIn some solid solutions this may result in only limited
admittance for the smaller (or larger) ionAs a result the structure
may reject the excess that it tolerated at higher temperatures The
process is exsolution and the product may be oriented lamellae of
the lesser complementary phase in the greater hostAlternatively the
exsolved material may be entirely rejected from the crystal, or
form as non-coherent masses
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ExsolutionThe process is exsolution and the product may be
oriented lamellae of the lesser complementary phase in the greater
host
Alternatively the exsolved material may be entirely rejected
from the crystal, or form as non-coherent masseswhispy perthite
lamellae as albite is exsolved from orthoclaseBlebby cpx exsolved
from opx host, Skaergaard Intrusion Opx with lamellae of exsolved
plagioclase, Nain anorthosite Opx with 2 lamellae of exsolved cpx,
Bushveld Intrusion From Deer et al Rock-Forming Minerals vol 1A.
WIley
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Order - Disorder
Random vs. ordered atoms 1. Random 2. Perfect OrderAlternating A
and B- Lower TNote larger unit cell!Each atom is statistically
identical (chance of being A is the same for each position) Higher
T
At 0 K entropy drops to zero and all solutions become perfectly
ordered at equilibriumAt higher temperatures solutions (even in
solids) become progressively disordered until they eventually
become completely disorderedThe degree of disorder is a function of
temperature, such that there is some equilibrium degree of disorder
for a given solution at a given temperature
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Order - Disorder
Triclinic monoclinic in KAlSi3O8 requires mirror symmetry
Must disorder at high temperature before monoclinicpotential
mirror
This is not a trivial concept that merely concerns
sub-microscopic propertiesThe triclinic monoclinic transition in
feldspar KAlSi3O8 requires that there is mirror symmetryIf Al and
Si are ordered on the IV sites (Al is grey in this picture, while
Si is blue), then no mirror is possibleMust disorder at high
temperature before can become monoclinicSome feldspars, if they are
heated rather slowly, may remain partially ordered, and thus will
not invert to the monoclinic form at the temperature predicted
(based on disordered feldspars)!
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Crystal DefectsDefects can affectStrengthConductivityDeformation
styleColor
All of our previous discussion is based on perfect crystalsNew
techniques of XRD and HRTEM have shown that defects are common in
crystalline substances
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Crystal DefectsSteel spheres:a) Regular packed array with 3
point defectsb) Point and line defectsc) Mosaic (or domains)
separated by defect boundariesThese are not twins!Fig 3.50 of Klein
and Hurlbut, Manual of Mineralogy, John Wiley and Sons
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Crystal Defects1. Point Defectsa) Schottky (vacancy) - seen with
steel balls in last frame
b) ImpurityForeign ion replaces normal one (solid solution)
Not considered a defectForeign ion is added (interstitial)Both
combined
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Crystal Defects1. Point Defects
c) Frenkel (cation hops from lattice site to interstitial)= a +
b combination
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Crystal Defects2. Line Defectsd) Edge dislocation
Migration aids ductile deformationFig 10-4 of Bloss,
Crystallography and Crystal Chemistry. MSA
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Crystal Defects2. Line Defectse) Screw dislocation (aids mineral
growth)Fig 10-5 of Bloss, Crystallography and Crystal Chemistry.
MSA
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Crystal Defects3. Plane Defectsf) Lineage structure or mosaic
crystalBoundary of slightly mis-oriented volumes within a single
crystalLattices are close enough to provide continuity (so not
separate crystals)Has short-range order, but not long-range (V4)Fig
10-1 of Bloss, Crystallography and Crystal Chemistry. MSA
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Crystal Defects3. Plane Defectsg) Domain structure (antiphase
domains) Also has short-range but not long-range orderFig 10-2 of
Bloss, Crystallography and Crystal Chemistry. MSA
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Crystal Defects3. Plane Defects
h) Stacking faultsCommon in clays and low-T disequilibriumA - B
- C layers may be various clay types (illite, smectite, etc.)
ABCABCABCABABCABCAAAAAABAAAAAAAABABABABABCABABAB
As temperature drops, the decreasing thermal energy in the
lattice, the tolerance of one end-member for the complementary ion
becomes lessIn some solid solutions this may result in only limited
admittance for the smaller (or larger) ionAs a result the structure
may reject the excess that it tolerated at higher temperatures The
process is exsolution and the product may be oriented lamellae of
the lesser complementary phase in the greater hostAlternatively the
exsolved material may be entirely rejected from the crystal, or
form as non-coherent masses
At 0 K entropy drops to zero and all solutions become perfectly
ordered at equilibriumAt higher temperatures solutions (even in
solids) become progressively disordered until they eventually
become completely disorderedThe degree of disorder is a function of
temperature, such that there is some equilibrium degree of disorder
for a given solution at a given temperature
This is not a trivial concept that merely concerns
sub-microscopic propertiesThe triclinic monoclinic transition in
feldspar KAlSi3O8 requires that there is mirror symmetryIf Al and
Si are ordered on the IV sites (Al is grey in this picture, while
Si is blue), then no mirror is possibleMust disorder at high
temperature before can become monoclinicSome feldspars, if they are
heated rather slowly, may remain partially ordered, and thus will
not invert to the monoclinic form at the temperature predicted
(based on disordered feldspars)!
All of our previous discussion is based on perfect crystalsNew
techniques of XRD and HRTEM have shown that defects are common in
crystalline substances